Rafael Benitez's Napoli went into the clash hoping to move up to third in the league as they targeted victory and a 12th successive league match without defeat.
But after a combination of Napoli's wastefulness in attack and Milan's clinical nature in front of goal, Inzaghi was the coach left rejoicing with pride at full-time.
Goals from Jeremy Menez and Giacomo Bonaventura ultimately proved decisive and Inzaghi was particularly impressed with the character displayed by his side, with Napoli enjoying a considerable amount of pressure.
He told Sky Sport Italia: "We've some extraordinary players out injured, including Italy’s first-choice full-backs and Alex, but I always believed in the team.
"Tonight's performance was a great display of character and I am very, very proud of these players.
"At times it disappoints me to hear criticism, as losing against Genoa on a set play can happen.
"We are on the right track and need to do a little more to reach the top spots, but I am very happy with the first goal [from Menez] as we had worked on that in training.
"It's always nice to see a training ground routine prove fruitful in a match situation.
"I complimented my team also for the attitude of the three who came off the bench [Cristian Zapata, Sulley Muntari and Michael Essien]. They went on foaming at the mouth to give their contribution.
"Clearly we need to improve our consistency, as we have ups and downs, but to beat a side that was targeting the title will really boost our confidence."
